Semi-peanian Characterizations of E2 and S2

The problem of characterizing the closed 2-cell E2 as an irreducible lc-connexe about a 1-sphere using unicoherence and not assuming compactness was proposed by Professor R. L. Wilder. It is found in Theorem 1 that a semi-peanian space in which all 1-spheres are contained in lc-connexes which are irreducible relative to certain unicoherence properties and satisfy a certain incidence relation and which is itself such a connexe is indeed a closed 2-cell. In Theorem 2 there is obtained a characterization of the closed 2-sphere S2 among the semi-peanian spaces. The author gratefully acknowledges his indebtedness to Professors R. L. Wilder and G. S. Young, Jr.